Abstract
The well known g-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the strong-Lefschetz property. We prove that the strong-Lefschetz property is preserved under the following constructions on homology spheres: join, connected sum, and stellar subdivisions. The last construction is a step towards proving the g-conjecture for piecewise-linear spheres.
| Original language | English |
|---|---|
| Pages (from-to) | 111-129 |
| Number of pages | 19 |
| Journal | Journal of Algebraic Combinatorics |
| Volume | 31 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2010 |
| Externally published | Yes |
Bibliographical note
Funding Information:Acknowledgements We deeply thank Satoshi Murai for his valuable comments on an earlier version of this paper, and Gil Kalai for helpful discussions. Further thanks go to the referees, especially one of them, whose detailed comments greatly helped to improve the presentation. Part of this work was done during the “Algebraic Combinatorics” program at the Institut Mittag-Leffler in Spring 2005. We are grateful to Anders Björner and Richard Stanley for inviting us to this program. The authors were partially supported by the European Commission’s IHRP Programme, grant HPRN-CT-2001-00272, “Algebraic Combinatorics in Europe”. Another part of this work was done during the special semester at the Institute for Advanced Studies in Jerusalem, in Spring 2007. We are grateful to IAS for the hospitality, and to Gil Kalai for organizing this semester.
Funding Information:
Research of E. Nevo was partially supported by an NSF Award DMS-0757828.
Keywords
- Face ring
- Homology sphere
- Strong-Lefschetz property